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Factor analysis, a popular method for interpreting multivariate data, models the covariance among p p variables as being due to a small number ( k k , 1 ≤ k > p 1 ≤ k > p ) of hidden variables. A factor analysis of Y Y can be thought of as an ordered or unordered collection, F ( Y ) F(Y) , of k k linearly independent lines in R p Rᵖ . Let Y ′ Y’ be the collection of data sets for which F ( Y ) F(Y) is defined. The “singularities” of F F are those data sets, Y Y , in the closure, Y ¯ ′ Ȳ’ , at which the limit, lim Y ′ → Y , Y ′ ∈ Y
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Steven P. Ellis (2004) studied this question.
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